本研究報告主要是改善邊界元方法在有支付補償金的連續型外匯雙障礙失效選擇權之定價問題。而此選擇權的合約內容有上下共兩個障礙價格,在到期日之前,若標的匯價碰觸到任何一邊的障礙價格時,則此選擇權立即失效,並且賣方必須支付買方一筆合約內簽定的報酬以作補償。

在本文中,首先介紹選擇權.外匯選擇權.障礙選擇權,接下來以Black-Scholes Model而衍生於外匯選擇權的Garman-Kohlhagen Model為數學模型,之後轉換成熱傳導邊界問題,並且設計一邊界元方法求出此邊界值問題,最後解得有支付補償金的外匯雙障礙失效選擇權的價格。

本文最後利用此邊界元方法實際計算出外匯雙障礙失效選擇權。

This study mainly improves the boundary element method on pricing a continuous type foreign double knock-out barrier option. That is, there are upper and lower barrier prices in this option. The double barrier option is knock-out, if the underlying foreign currency price touches any of them before the expiration day. And the seller must pay the buyer rebate which was decided in the contract.
In this paper, we first introduce options, foreign currency options,and barrier options. The mathematical model is Garman-Kohlhagen Model with foreign currency options which is developed from Black-Scholes Model, then it is converted to a boundary value problem with the heat equation. And designing a boundary element method deal with the boundary value problem to get a foreign double knock-out barrier option price with rebate.
Finally, pricing a foreign double knock-out barrier call value by the boundary element method of this paper.

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